A143466 Odious count triangle, T(n,k) = A010060(n) * A010060(k); 1 <= k <= n.

1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1

Offset

1,1

Comments

Row sums = (1, 2, 0, 3, 0, 0, 4, 5, 0, 0, 0, 6, ...) = A102390, the Odious count sequence starting with offset 1.

Odious count triangle, T(n,k) = A010060(n) * A010060(k); 1 <= k <= n. If n is an odious number (1, 2, 4, 7, 8, ...), row n consists of the first n terms of the M-T sequence (A010060) starting with offset 1: (1, 1, 0, 1, 0, 0, 1, 1, ...); otherwise 0. Let X be an infinite lower triangular matrix with (1, 1, 0, 1, 0, 0, 1, ...) in the main diagonal and the rest zeros (i.e., A010060 * 0^(n-k), with offset 1). Then X * A000012 * X = triangle A143466.

Links

Table of n, a(n) for n=1..91.

Example

First few rows of the triangle:
  1;
  1, 1;
  0, 0, 0;
  1, 1, 0, 1;
  0, 0, 0, 0, 0;
  0, 0, 0, 0, 0, 0;
  1, 1, 0, 1, 0, 0, 1;
  ...
T(7,3) = 1 since given the first few terms of the M-T sequence starting with offset 1, (1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 1, ...), product of 7th and 3rd terms = 1.

Mathematica

T[n_, k_] := ThueMorse[n] * ThueMorse[k]; Table[T[n, k], {n, 1, 13}, {k, 1, n}] // Flatten (* Amiram Eldar, Aug 05 2023 *)

Crossrefs

Cf. A000012, A010060, A102390.

Sequence in context: A068431 A266978 A074201 * A195053 A267136 A117908

Adjacent sequences: A143463 A143464 A143465 * A143467 A143468 A143469

Keyword

nonn,tabl

Author

Gary W. Adamson, Aug 17 2008

Extensions

More terms from Amiram Eldar, Aug 05 2023

Status

approved